# 20.2.1 Magnetic Flux

### Magnetic Flux Definition

• Electromagnetic induction is when an e.m.f is induced in a closed circuit conductor due to it moving through a magnetic field
• This happens when a conductor cuts through magnetic field lines
• The amount of e.m.f induced is determined by the magnetic flux
• This is the total magnetic field that passes through a given area
• It is a maximum when the magnetic field lines are perpendicular to the area
• It is at a minimum when the magnetic field lines are parallel to the area
• The magnetic flux is defined as:

The product of the magnetic flux density and the cross-sectional area perpendicular to the direction of the magnetic flux density

• In other words, magnetic flux is the number of magnetic field lines through a given area

### Calculating Magnetic Flux

• Magnetic flux is defined by the symbol Φ (greek letter ‘phi’)
• It is measured in units of Webers (Wb)
• Magnetic flux can be calculated using the equation:

Φ = BA

• Where:
• Φ = magnetic flux (Wb)
• B = magnetic flux density (T)
• A = cross-sectional area (m2)
• When the magnet field lines are not completely perpendicular to the area A, then the component of magnetic flux density B perpendicular to the area is taken
• The equation then becomes:

Φ = BA cos(θ)

• Where:
• θ = angle between magnetic field lines and the line perpendicular to the plane of the area (often called the normal line) (degrees)
• This means the magnetic flux is:
• Maximum = BA when cos(θ) =1 therefore θ = 0o. The magnetic field lines are perpendicular to the plane of the area
• Minimum = 0 when cos(θ) = 0 therefore θ = 90o. The magnetic fields lines are parallel to the plane of the area
• An e.m.f is induced in a circuit when the magnetic flux linkage changes with respect to time
• This means an e.m.f is induced when there is:
• A changing magnetic flux density B
• A changing cross-sectional area A
• A change in angle θ

Part (a)

Step 1:            Write out the known quantities

Cross-sectional area, A = 40 cm × 73 cm = (40 × 10-2) × (73 × 10-2) = 0.292 m2

Magnetic flux density, B = 1.8 × 10-5 T

Step 2:             Write down the equation for magnetic flux

Φ = BA

Step 3:            Substitute in values

Φ = (1.8 × 10-5) × 0.292 = 5.256 × 10-6 = 5.3 × 10-6 Wb

Part (b)

The magnetic flux will be at a minimum when the window is opened by 90o and a  maximum when fully closed or opened to 180o

#### Exam Tip

Consider carefully the value of θ, it is the angle between the field lines and the line normal (perpendicular) to the plane of the area the field lines are passing through. If it helps, drawing the normal on the area provided will help visualise the correct angle. ### Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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